The Bandai WonderSwan was a competitor to the Game Boy (interestingly, both were created by the same guy) that never made it outside of Japan, and so it doesn't have many games in English. Much of its titles are anime-licensed and RPGs, but it also has a decent number of (import-friendly) fighters, platformers, and action games.

The WonderSwan comes in three versions: the monochrome classic, the Color, and the Crystal. The Color and Crystal run on the same hardware, but the Crystal has a superior TFT screen and shorter battery life. All of them run on a single AA battery, with the following expected life:

Classic: 30–40 hours

Color: 20 hours

Crystal: 12 hours

There are also AC adapter and rechargeable battery pack accessories for those who'd prefer less battery expenditure.

Drop some phat beats in a game that should need no introduction. Seems like it's in black and white only, but the sound is surprisingly impressive! Take a listen for yourself.

Bistro Recipe

RPG

It's like Pokemon but you make your own monsters, really good spritework and high difficulty. You may vaguely remember seeing the anime localized as "Fighting Foodons".

Blue Wing Blitz

Strategy

Excellent strategy game by Square, the graphical quality is just amazing it looks like a GBA game.

Chocobo no Fushigina Dungeon

RPG / Dungeon Crawler

A port of the Playstation game in nice monochrome 2D, just as good but some prefer this for portability and such.

Dicing Knight Period

RPG / Dungeon Crawler

Infamously rare dungeon crawler that has some damn good gameplay. It's also very fast paced for the genre, especially impressive given the hardware at the time. This game has a translation patch for the ROM, but it's so rare, that even the ROM itself can be hard to find! Still, check this out and you'll see why so many have begun the trek to hunt it down.

Digimon Tamers: Battle Spirit (Ver. 1.5)----

Battle Spirit: Digimon Frontier

Fighting/platformer

There are three Battle Spirit games on the WonderSwan (all in color), and they're all fighting games in platform-filled arenas, like Smash Bros. or the Jump games on DS. Instead of health, you grab your opponents' balls ("D-Spirits") which fly out in varying amounts when hit, while trying not to get your own balls grabbed. The first and third games were lazily ported to the GBA in English (a static border makes up the difference in screen size), but Ver. 1.5 (pictured), an enhanced version of the first game, is still only available here. They're all fun and easy to play regardless of the language and Digimon barriers.

Final Fantasy 1 / 2 / 4

RPG

Pretty cool ports/remakes of the SNES/NES games, lots of the sprite work is redone and improved. In FF1/FF2 the alot of glitches and bugs were fixed, and weapons acted how they should have (i.e. exploit enemy weaknesses). In FF4, you can choose between the original and easytype versions. These were used as the basis for the PS1/GBA remixes, which added much more extra content. Still, they're interesting to try if you ever wanted to hear how the music might have sounded in 8-bit-esque sound.

Ganso Jajamaru-kun

Platformer

A remix/remake of the NES game with improved controls and monochrome graphics.

Guilty Gear Petit 1 & 2

Fighting

That funky fast-paced fighter now in bite-size form. The action has transferred impressively well, the graphics are amusingly/accurately re-recorded in SD style, and the music, though not as rockin' still retains the flavor of melodies nicely enough. Sadly, there's only a small handful of characters as a result, but these do have an exclusive character not seen in the main series.

Hataraku Chocobo

Life Sim

Roughly translated: "Working Chocobo" or "Chocobo on the Job". You raise a Chocobo while "completing various tasks to earn items." Most of these tasks seem related to farming or building up a town. Not to be confused with Dice de Chocobo, a board game, that was canceled before it was released on this (but ended up on PS1).

Judgement Silversword -Rebirth Edition-

Shoot 'em Up

A fast-paced score attack game with heavy focus on aggressive play through eliminating enemies quickly. Your shield cancels bullets and destroys enemies, yielding multipliers, but recharges slowly, requiring a bit of tactical use. Available as a port on the Eschatos 360 release alongside its sequel Cardinal Sins. Somewhat of a rarity in cartridge form as it received a limited reprint, being made by an independent developer on the WonderWitch development kit, though it's easy to emulate.

Klonoa: Midnight Museum

Platformer

A decent entry in the Klonoa series. Unfortunately it's pretty easy, and there's NO BOSSES. Still, if you want some double-jumping and wind-bullets for your Wonderswan, here ya go. This is pretty much the basis for the GBA platformers though, which ended up addressing the few problems with this.

Makaimura for WonderSwan

Platformer

An original game that basically remixes content from the first game (so no magic, double jumps, or aiming) with new bosses and level design. It's well animated and the action is spot-on, but enemies tend to spawn like the dickens and bosses have tiny hit-boxes require some damn precise shooting, versus that of others in the series. Thankfully, Arthur has the power to rapid-fire all of his weapons to help even the odds, but he'll need your skills to get over those perilous platforms!

Makai Toushi SaGa

RPG

Excellent remake of Final Fantasy Legend for the Game Boy. This version jacks up the graphics to SNES-like levels (though the music is still 8-bit sounding, it's also improved a bit, too) and is totally worth the $5 bucks or so that your average Wonderswan game costs. And yeah, you can still exploit the chainsaw for the final boss.

It's basically a port of the original, without any extra bells and whistles. Drill to the bottom, match colored blocks to get there faster, and try not to run out of air. At least it's in color and not as squished as other early portable ports!

Namco Super Wars

Tactical RPG

A title that's vaguely like the Super Robot Wars series, but has some interesting action-based aspects of its own. Use various Namco characters and their skills to defeat the threat of evil. Namco x Capcom for the PS2 used this as a basis and expanded upon it, both gameplay and roster-wise.

One Piece: Chopper no Daibouken

Rougelike/Action-RPG

The One Piece cast has been turned into animals and its up to their reindeer-moose mascot thing to help them return to humans. Thankfully, they haven't lost all their powers, and can offer some assistance. However, Chopper himself does most of the work. Curiously, there's a number of action-based segments that are not tile-based, such as boss battles, mini-game exploration segments, and bonus games. Even if you're not a fan, you may want to check this out.

Pocket Fighter

Fighting

The only handheld port of the game, and it's a damn good one too. Features all the characters, but this game is one of the most expensive.

Puyo Puyo Tsuu

Puzzle

[description goes here]

Romancing SaGa

RPG

Port of the SFC/SNES classic with a few extras. The series proper is known for its numerous attacks and avant-garde leveling system, both of which are quite cool once you get the hang of them. In addition, the narratives are not entirely linear, giving you numerous story-based choices to select, many of which change the path your adventure follows. In addition, there's also the super-rad music by Kenji Ito, which sounds good even on the Wonderswan.

Slither Link

Puzzle

Monochrome version of the number-based newspaper puzzle. Create a single circuit around the grid using the clues offered and logic. A decent version of the game and not too tough to learn the menus for, but busy, black and white graphics can sometimes make it hard to tell what you're looking at.

Tekken Card Challenge

Fighting

A strange title revolving around using cards as attacks. There's also an adventure mode where you explore dungeons in a roguelike-ish environment.

Tetris

Puzzle

Pretty standard Tetris version. The graphics are fine, music includes the standard Korobeiniki, and the menus are all in English. Has Hold and shows the next three pieces. For Tetris nerds: follows the "Tetris Guideline".

Wild Card

Card Game

Another original Square title for the system. Everything is done with cards, from navigation to combat. Pretty artwork.